Global well-posedness for the 1D cubic nonlinear Schrödinger equation in L^p, p>2

2025/06/10 by Ryosuke Hyakuna, Hyakuna, Ryosuke
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2506.08554

Abstract

In this paper, we show that the one dimensional cubic nonlinear Schrödinger equation is globally well posed in L^p for 2≤ p <13/6. In particular, we prove that the global solution enjoys the persistence property for a twisted variable at any time, which implies the result is a natural exetension of the classical global well-posedness in L² to L^p. The proof exploits the data-decomposition argument originally developed by Vargas-Vega in the functional framework introduced by Zhou.

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